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Object detection is one of the core tasks of computer vision, and bounding box (bbox) regression is one of the basic tasks of object detection. In recent years of related research, bbox regression is often used in the Intersection over Union (IoU) loss and its improved version. In this paper, for the first time, we introduce the Dice coefficient into the regression loss calculation and propose a new measure which is superior to and can replace the IoU. We define three properties of the new measure and prove the theory by mathematical reasoning and analysis of the existing work. This paper also proposes the N-IoU regression loss family. And the superiority of the N-IoU regression loss family is proved by designing simulation experiments and comparative experiments. The main results of this paper are: (1) The proposed new measure is better than IoU which can be used to evaluate bounding box regression, and the three properties of the new measure can be used as a broad criterion for the design of regression loss functions; and (2) we propose N-IoU loss. The parameter n of N-IOU can be debugged, which can be widely adapted to different application scenarios with higher flexibility, and the regression performance is better. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger's inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

A lot of research has validated that zeroing neural network (ZNN) model is a reliable tool for solving time-varying problems. Generally, convergent performance is often one of the most important measures for the practicability of the ZNN model. Besides, its practicability is also up to its anti-noise ability in the process of solving time-varying problems. It is worth noting that numerous existing ZNN models perform well in terms of the above two issues. In order to further enhance the robustness and convergence of the ZNN model, two novel activation functions (novel activation function-1 (NAF-1) and novel activation function-2 (NAF-2)) are designed. Based on the above two NAFs, two robust ZNN models (zeroing neural network-1 (ZNN-1) and zeroing neural network-2 (ZNN-2)) with fixed time convergence and strong robustness to noise for solving time-varying Sylvester equation (TVSE) are proposed in this paper. The robustness and convergence of the two proposed ZNN models are verified by rigorous mathematical analysis, and their practicability are validated by three simulation experiments (second-order and third-order TVSE solving and manipulator trajectory tracking). All the studies indicate that the two ZNN models can quickly find the accurate solution of TVSE in noiseless and noisy environment. [ABSTRACT FROM AUTHOR]

Mathematical model-based analysis and control of human immunodeficiency virus (HIV) infection have recently provided important advantages in medicine. In this paper, firstly the literature on mathematical models and applied control methods will be surveyed to evaluate the HIV models and therapy. Secondly, a cubature Kalman filter-based nonlinear model predictive control is proposed for the multi-input multi-output control of HIV infection for decreasing the cost of sensory devices and increasing the efficiency of therapy. By doing so both unmeasurable states and personalized parameters of the HIV infection are jointly estimated in a control process to generate suitable drug dosages. In the literature, the applied drug dosages are in continuous or on/off levels. For a practical application of continuous drug dosage-level, it has been discretized into 10 levels of full dosage level. Therefore, the applied drug dosages are in piecewise-continuous levels instead of continuous values or on/off levels. The proposed observer–controller configuration has been applied to the strong and moderate therapy levels of long-term non-progressive as well as fast-progressive patients with personalized parameters, where the application results are discussed for 1-, 5-, 10- and 20-year periods. The computational results show that satisfactory performances are obtained for future applications in terms of the root-mean-squared error of the estimation and control, and in terms of the integral sum of the control input. [ABSTRACT FROM AUTHOR]

This paper focuses on the lag synchronization issue for a kind of general complex networks with multiple time-varying delays via the pinning control strategy. By applying the Lyaponov functional theory and mathematical analysis techniques, sufficient verifiable criteria that depend on both intrinsic time-varying delay and coupled time-varying delay are obtained to achieve lag synchronization of the networks. Moreover, the coupling configuration matrices are not required to be symmetric or irreducible, and the minimum number of pinned nodes is determined by node dynamics, coupling matrices, and the designed parameter matrices. Finally, a numerical example is given to illustrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

Effective dimension, an indicator for the difficulty of high-dimensional integration, describes whether a function can be well approximated by low-dimensional terms or sums of low-order terms. Some problems in option pricing are believed to have low effective dimensions, which help explain the success of quasi-Monte Carlo (QMC) methods recently observed in financial engineering. This paper provides a way of studying the structure of effective dimensions by finding a proper space the function of interest belongs to and then determining the effective dimension of that space. To this end, we extend the definitions of effective dimensions to weighted function spaces with product-order-dependent weights and give bounds on norms and variances. Furthermore, we show that the proposed method is applicable to functions arising in option pricing and consequently offers some hints on the performance of QMC methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the lag quasi-synchronization for memristive neural networks (MNNs) with switching jumps mismatch. The inherent characteristic of MNNs is fully taken into account. Based on Lyapunov-Krasovskii functional and differential inclusions theory, intermittent control approach is utilized to realize the exponential lag quasi-synchronization of the considered model. The error level is closely related to the switching jumps. In addition, a simple design procedure of controller is presented to ensure that the synchronization error between the master system and the slave system converges to a predetermined level. Two numerical examples are offered to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Machining operations involving complex multivariate parameters are defined by many machining parameters. Correct selection of these parameters is crucial for an efficient and economical cutting operation. The grooving operation required in many cases is one of the most problematic methods in all metal cutting operations, especially in terms of chip control. This paper covers theoretical analysis and mathematical modeling of deformation and stresses of the grooving tool. Cutting forces affecting the service life of the grooving tool were measured by various cutting experiments. Deformation and stresses of grooving tool caused by cutting forces were analyzed by finite element method using Ansys software. In modeling with artificial neural networks (ANN), grooving insert width, cutting speed, feed rate, radial force and primary cutting force are inputs in the model and deformation and stresses of the grooving tool are outputs. An algorithm, which is a Matlab script file, was developed to determine the optimal combination of neural network parameters such as the normalization method, number of hidden neurons, transfer function and training algorithm. The best-fitting set determined by the algorithm developed for the model was achieved with the Levenberg–Marquardt backpropagation algorithm, logistic sigmoid transfer function, nine hidden neurons and normalization method with a scaling factor. The MSE, R2, MAPE values of the ANN model are 2.0327 × 10−6, 0.999992 and 0.379227, respectively. Performance results have shown that the proposed approach can also be used for ANN modeling of machining parameters in other cutting operations other than grooving. [ABSTRACT FROM AUTHOR]

A Bloom filter is a special case of an artificial neural network with two layers. Traditionally, it is seen as a simple data structure supporting membership queries on a set. The standard Bloom filter does not support the delete operation, and therefore, many applications use a counting Bloom filter to enable deletion. This paper proposes a generalization of the counting Bloom filter approach, called "autoscaling Bloom filters", which allows adjustment of its capacity with probabilistic bounds on false positives and true positives. Thus, by relaxing the requirement on perfect true positive rate, the proposed autoscaling Bloom filter addresses the major difficulty of Bloom filters with respect to their scalability. In essence, the autoscaling Bloom filter is a binarized counting Bloom filter with an adjustable binarization threshold. We present the mathematical analysis of its performance and provide a procedure for minimizing its false positive rate. [ABSTRACT FROM AUTHOR]

Bat algorithm (BA) is a new approach designed by imitating bat's behavior of searching and capturing preys. The existing results have demonstrated the effectiveness and efficiency in comparison with other heuristic algorithms such as genetic algorithms and particle swarm optimization. In this paper, we design a novel framework for bat algorithm named two-stage bat algorithm (TSBA) using a trade-off strategy which balances the relationship between exploration and exploitation at the most extent. Inspired by the multi-population methods (e.g., artificial bee colony), we not only concern some technologies to avoid premature inevitably encountered when using BA, but also use a trade-off strategy to improve the comprehensive search performance for optimization. Some typical test sets which consist of 27 benchmark functions are utilized in comparative experiment, and the simulation results in terms of convergence rate and accuracy illustrate that the TSBA has a competitive performance than other swarm intelligent optimization algorithms. In addition, the proposed algorithm will not lend to the tremendous increase in computing time and thus will be a powerful tool in practical applications. [ABSTRACT FROM AUTHOR]

Neural networks are widely deployed in many scenarios and have reached or exceeded human-level performance in some tasks. However, the researchers found that existing neural networks are vulnerable to attacks. One of the cases is that the network outputs the wrong result in the presence of small perturbations in the input. It indicates that the neural network does not meet the robustness. Neural networks, which do not meet robustness, will limit their application in safety-critical systems such as automatic driving and wise medical. Hence, the research on the robustness of neural networks is significant. Interval analysis is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation and can be used to calculate the exact output range of a real-valued function. Based on the theoretical framework of interval analysis, we define the interval extension of neural networks and prove that it includes the inclusion isotonicity and Lipschitzian property. It illustrates the feasibility of using interval extension to compute the output range of a neural network corresponding to a given input range. In order to evaluate the robustness of the neural network, we further analyze the characteristics of the neural network interval extension and design a neural network robustness evaluation method based on the greedy strategy. Experiment results on the MNIST and ACAS Xu datasets show that the method can effectively evaluate the robustness of the neural network with good time performance. [ABSTRACT FROM AUTHOR]

In this article, we investigated a class of genetic regulatory networks (GRNs) with time-varying delays and Stepanov-like weighted pseudo-almost automorphic coefficients. By Banach fixed point theorem, we firstly established the existence results of the weighted pseudo-almost automorphic solutions for the proposed GRNs. Secondly, by using suitable Lyapunov functional and mathematical analysis skills, new criteria are derived for ensuring the global exponential stability of the solutions. Finally, a numerical example and remarks are provided to substantiate the efficiency of obtained results. The derived results of this article are new and complement many earlier works and the ideas of this work can be applied to investigate other similar systems. [ABSTRACT FROM AUTHOR]

Many problems arising in different fields of sciences and engineering can be reduced, by applying some appropriate discretization, either to a system of integrodifferential algebraic equations or to a sequence of such systems. The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space, for obtaining the solutions of integrodifferential algebraic systems of temporal two-point boundary value problems. Two extended inner product spaces W[0, 1] and H[0, 1] are constructed in which the boundary conditions of the systems are satisfied, while two smooth kernel functions Rt(s) and rt(s) are used throughout the evolution of the algorithm in order to obtain the required grid points. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing kernel theory. In this approach, computational results of some numerical examples are presented to illustrate the viability, simplicity, and applicability of the algorithm developed. [ABSTRACT FROM AUTHOR]

A soft matrix multiplication of matrices in different types was not possible so far. In this study, we generalize the soft matrix products And, And-Not, Or, Or-Not defined in Çağman and Enginoğlu (Comput Math Appl 59:3308-3314, 2010) so as to multiply soft matrices in different types. Furthermore, these generalizations allow us to multiply soft matrices more than two soft matrices. Therefore, we can solve decision making problems with multiple decision makers using a single product. These new operations make the process of solving decision making problems faster, easier and more convenient. Then we construct some effective decision making methods called soft distributive max-min (max-max, min-min, min-max) decision making methods. We also provided Scilab codes to demonstrate our methods. [ABSTRACT FROM AUTHOR]

In this study, cuckoo search is introduced for performing the parameter estimation of shallow wave equation for the first time. Cuckoo search (CS) is invented based on the inspiration of brood parasitic behavior of some cuckoo species in combination with the Lévy flight behavior. These meta-heuristics have been successfully used for solving some optimization problems with promising results. However, this emerging optimization method has not been applied in parameter inversion problem. This study reports a CS-based parameter estimation method to inverse the roughness coefficient and the coefficient of eddy viscosity under some specific conditions. Simulation results and experimental data show that cuckoo search offers a reliable performance for these parameter estimation problems. [ABSTRACT FROM AUTHOR]

We consider the supervised pattern classification in the high-dimensional setting, in which the number of features is much larger than the number of observations. We present a novel approach to the sparse Fisher linear discriminant problem using the $$\ell _0$$ -norm. The resulting optimization problem is nonconvex, discontinuous and very hard to solve. We overcome the discontinuity by using appropriate approximations to the $$\ell _0$$ -norm such that the resulting problems can be formulated as difference of convex functions (DC) programs to which DC programming and DC Algorithms (DCA) are investigated. The experimental results on both simulated and real datasets demonstrate the efficiency of the proposed algorithms compared to some state-of-the-art methods. [ABSTRACT FROM AUTHOR]